All LVP is actually waterproof. It's a very solid option for basement flooring because of this. That being said though, remember that you should never leave water sitting on your flooring, whatever that flooring, for weeks on end. The water won't damage you LVP, but it will eventually seep through to the bottom floor and gradually cause damage and become a huge insurance problem. You can measure against this though with the installation of a moisture trap depending on your situation. Another thing about LVP, is the option of ER or Embossed in Register. With ER, the texture of the plank matches up perfectly with the register or the original graphic. This means that every grain is captured in detail, including wood knots. An advantage of this is increased surface area so it protects against slipperiness and you from falling. Here's the main link I used to learn about ER and LVP if you'd like more information. I hope this helps!: https://www.reallycheapfloors.com/blog/the-best-flooring-for-basements/

OK...let's look at budget. You have 210sf of space. You will want to purchase 10% more for waste/damaged/unusable planks. That means you need to purchase 231sf (to the nearest box). Now let's look at budget per square foot: $1000/231sf = $4.32/sf total costs. The cork will do very well with this. At $2.78/sf + $1/sf for transport you are still at $3.78/sf. What's the underlay?

I understand what the SALES PITCH says. I know. They HYPE THE SNOT out of these floors but once you get down to the installation instructions, it says the floor must be SMOOTH and FLAT! Of course any floor can go over anything that is smooth and flat. The problem comes in when the subfloor (your stained concrete) is NOT smooth, NOT flat and needs fixing. All subfloors require a bit of a fix. Every. Single. One. Great. Now that has been cleared up, let's look at YOUR concrete and why it will require MORE work than a regular dusty ol' cement slab. A cement slab (dusty one...no finish) will require some NORMAL amount of grinding and a NORMAL amount of filling with Self Leveling Compound (SLC). The SLC needs to stick or to 'grab' the old concrete. That means the concrete needs to be roughed up (ground a bit or shot blasted if it is REALLY terrible). Then the SLC can have a NEW surface to grab...which it does nicely. The FINISH on your floor (and the reapplication of more finish 8 years ago) is a product that PREVENTS other things from sticking. Notice how your newest finish is peeling? Right. Now imagine that happening to the SLC that is used to flatten the concrete. Oh dear. What a crumbling, gritty, nasty mess. Floors have to come up and things need to be done properly. When it comes to finished concrete floors like yours (not just stained...but FINISHED) they must have the FINISH and the STAIN removed before the SLC can be added. The good news is you don't have to do the WHOLE thing. You just need to grind it off on the HUMPS (because they sit too tall = not flat) and the hollows (because you need the SLC to stick). That's when the hollows are skim coated with SLC. It dries and then another light sanding to the new SLC = ready to rock a new flooring product. A traditional concrete slab requires $2-$4/sf worth of subfloor prep before a floating floor can be put down. Your concrete might need a snick more help...which could put it into the $4-$5/sf range for the prep. Once the subfloor is FLAT and SMOOTH you can now float whatever floor you want. See? You can put those floors over concrete....so long as it is flat and smooth.

I would have the tile removed, and get the floor sturdy and leveled and go with your idea of tile, in the bathroom. If you are talking about the rest of the house also, your best option would be to recarpet, if you dont have level floors.